GATE CSE 2012 | Combinatorics Question 11 | Discrete Mathematics

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GATE CSE 2012

MCQ (Single Correct Answer)

-0.3

The recurrence relation capturing the optional execution time of the Towers of Hanoi problem with $$n$$ discs is

$$T\left( n \right) = 2T\left( {n - 2} \right) + 2$$

$$T\left( n \right) = 2T\left( {n - 1} \right) + n$$

$$T\left( n \right) = 2T\left( {n/2} \right) + 1$$

$$T\left( n \right) = 2T\left( {n - 1} \right) + 1$$

GATE CSE 2004

MCQ (Single Correct Answer)

-0.3

In a class of 200 students, 125 students have taken Programming Language course, 85 students have taken Data Structures course, 65 student have taken Computer Organization coures; 50 students have taken both Programming Language and Data Structures, 35 students have taken both Programming Languages and Computer Organization; 30 students have taken both Data Structures and Computer Organization; 15 students have taken all the three course.

How many students have not taken any of the three courses?

GATE CSE 2003

MCQ (Single Correct Answer)

-0.3

$$m$$ identical balls are to be placed in $$n$$ distinct bags. You are given that $$m \ge kn$$, where $$k$$ is a natural number $$ \ge 1$$. In how many ways can the balls be placed in the bags if each bag must contain at least $$k$$ balls?

$$\left( {\matrix{ {m - k} \cr {n - 1} \cr } } \right)$$

$$\left( {\matrix{ {m - kn + n - 1} \cr {n - 1} \cr } } \right)$$

$$\left( {\matrix{ {m - 1} \cr {n - k} \cr } } \right)$$

$$\left( {\matrix{ {m - kn + n + k - 2} \cr {n - k} \cr } } \right)$$

GATE CSE 2003

MCQ (Single Correct Answer)

-0.3

$$n$$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The number of different gatherings possible at the party is

$$\left( {\matrix{ {2n} \cr n \cr } } \right) * {2^n}$$

$${3^n}$$

$${{\left( {2n} \right)!} \over {{2^n}}}$$

$$\left( {\matrix{ {2n} \cr n \cr } } \right)$$

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